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I have the following problem: Show that for [tex]m,n \geq2[/tex],

[tex]\left(\begin{array}{cc}m+n\\2\end{array}\right) = \left(\begin{array}{cc}m\\2\end{array}\right) + \left(\begin{array}{cc}n\\2\end{array}\right) + mn[/tex]

by using the formula

[tex]\left(\begin{array}{cc}a\\b\end{array}\right) = \frac{a!}{(a - b)!b!} [/tex]

and algebra.Prove it again without using this formula.

The first part was quite easy, but I am not sure how I could solve the second (bold) part without using a formula. Am I supposed to use a definition or something of that nature? I just am not seeing it, any ideas would be appreciated. Thanks

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# Homework Help: N choose k like problem

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